Hot gas engines of the Stirling type have been primarily external combustion engines employing pistons and cylinders. State of the art hot gas engines with pistons that are configured to turn drive shafts are designed with hot and cold cylinders, and a heat regenerator connected between the hot and cold cylinders. Separate hot and cold cylinders increase cost. Extensive developmental work has been carried out on hot gas engines because of their promise of high thermal efficiency. However, the hot gas engines developed so far have not succeeded in achieving the high thermal efficiency that is potentially possible. The inability to achieve high thermal efficiency is primarily because existing state of the art hot gas engines do not have their heat regenerators and their working gas processing steps designed for optimum heat regeneration. U.S. Pat. No. 4,455,825 pointed out that the working gas processing steps, and consequently the heat regeneration were not optimum. The heat regeneration was not optimum because working gas flowed between the hot and cold cylinders during the expansion and compression steps. Working gas that is present in, or that flows into the cold cylinder during the expansion step, and the working gas that is present in or flows into the hot cylinder during the compression step, produce negative work loops, and negatively impact the thermal efficiency. The working gas crossover issues were solved in U.S. Pat. Nos. 4,455,825 and 4,676,067. However, the engines in those patents did not address the role and design of the heat regenerator, and the engines in those patents continued to use separate hot and cold cylinders. The hot gas engines proposed in this disclosure are designed around the heat regenerator, and do not use separate hot and cold cylinders. In the engines proposed in this disclosure, the cold cylinder used in prior hot gas engines is replaced with a heat rejection means or cooler, and the hot cylinder is replaced with generalized pressure variation means.